• hemp3quilt posted an update 4 months ago

    4a) pˆ1=1−m11+a1+b1a1(1−ϑ1)a1(1−ϑ1)+rW14,1a1(1−ϑ1)+b1(1−σ1)+rW14,1, equation(3.4b) qˆ1=1−m11+a1+b1b1(1−σ1)b1(1−σ1)+rW14,1a1(1−ϑ1)+b1(1−σ1)+rW14,1, equation(3.4c) Dˆ1=m11+a1+b1a1(1−ϑ1)+b1(1−σ1)+rW14,1, equation(3.4d) pˆ2=m21−a2−b2−a2(1+ϑ2)−a2(1+ϑ2)+rW14,2−a2(1+ϑ2)−b2(1+σ2)+rW14,2, equation(3.4e) qˆ2=m21−a2−b2−b2(1+σ2)−b2(1+σ2)+rW14,2−a2(1+ϑ2)−b2(1+σ2)+rW14,2, equation(3.4f) Dˆ2=m21−a2−b2−a2(1+ϑ2)−b2(1+σ2)+rW14,2. It should be noted that, to this order of approximation, allele frequencies and LD in deme kk depend only on the selection and dominance parameters in deme kk. From the assumptions (2.5) and (2.6) on the selection coefficients, and assumption (2.2) on the dominance coefficients, it follows easily that Fm exhibits positive LD and that tighter linkage increases LD and elevates the equilibrium frequency of the locally adaptive alleles within the respective deme; Erlotinib molecular weight see (A.3). It is well known that in the absence of migration and of additive epistasis, no LD can be maintained. Also migration cannot generate or maintain LD in the presence of recombination (Bürger, 2009a). Therefore, LD is generated by the interaction of (nonepistatic) selection and migration. Increasing dominance of a locally adaptive allele decreases its frequency in the deme where it is advantageous (A.4). The reason is that the deleterious effect of the other allele is masked. Finally, increasing dominance of the locally adaptive alleles elevates the amount of LD in their respective deme and decreases the frequency of the haplotype with highest local fitness; see (A.5). Because in an isolated population subject to the selection scheme (2.1) there are four equilibria (the monomorphic states), in the full two-deme model with migration absent there are 16 equilibria. These are the four monomorphisms Mi(3.1), eight single-locus polymorphisms, F0 and three other (unstable) full polymorphisms; see Appendix A.1.2 for details. The monomorphisms and the single-locus polymorphisms are unstable with respect to the full state space S4×S4S4×S4. If the dominance coefficients satisfy equation(3.5) −1<ϑk<1and−1<σk<1  for  k=1  and  k=2, all equilibria are hyperbolic in the absence of migration (results not shown). Hence, the results of Karlin and McGregor (1972) imply that, for sufficiently weak migration (where ‘sufficiently’ may depend also on the dominance coefficients), there is at most one admissible equilibrium in the neighborhood of each equilibrium of the unperturbed system. Because unstable equilibria may leave the state space if migration is turned on, the number of admissible equilibria with migration is (much) smaller than 16. If the dominance coefficients satisfy (3.5), four of the eight single-locus polymorphisms and the three unstable full polymorphisms leave the state space when migration is turned on (Appendix A.1).